In Lickorish's 'An Introduction to Knot Theory' after Proposition 6.3 one reads:
Now suppose that $F$ is a Seifert surface for an oriented link $L$ in $\mathbb{S}^3$, so that $\partial F=L$. Let $N$ be a regular neighbourhood of $L$, a disjoint union of solid tori that 'fatten' the components of $L$. Let $X$ be the closure of $\mathbb{S}^3-N$. Then $F\cap X$ is $F$ with a (collar) neighbourhood of $\partial F$ removed. Thus $F\cap X$ is just a copy of $F$ and, just to simplify notation, it will be regarded as actually being $F$. This $F$ has a regular neighbourhood $F\times [-1,1]$ in $X$, with $F$ identified with $F\times 0$ and the notation chosen so that the meridian of every component of $L$ enters the neighbourhood at $F\times -1$ and leaves it at $F\times 1$.
I would mainly like to ask if someone is able to give me a little sketch/picture of what's going on here any why we have 'Then $F\cap X$ is $F$ with a (collar) neighbourhood of $\partial F$ removed.'?
Take $L$ to be the unit circle sitting in some plane in $\mathbb{R}^3$, and $F$ to be the unit disk in that plane. Then $N$ is a solid torus (thickened $L$) which "cuts" into $F$ near the boundary $\partial F = L$. That's the visual to see how the collar neighborhood of $\partial F$ sits inside $N$. Because $N$ has a radial coordinate (measured as distance away from $L$), and so along $F$ this radial coordinate defines the collar neighborhood of $F$.